What is the Greatest Common Factor of 45200 and 45220?

Greatest common factor (GCF) of 45200 and 45220 is 20.

GCF(45200,45220) = 20

We will now calculate the prime factors of 45200 and 45220, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45200 and 45220.

How to find the GCF of 45200 and 45220?

We will first find the prime factorization of 45200 and 45220. After we will calculate the factors of 45200 and 45220 and find the biggest common factor number .

Step-1: Prime Factorization of 45200

Prime factors of 45200 are 2, 5, 113. Prime factorization of 45200 in exponential form is:

45200 = 2⁴ × 5² × 113¹

Step-2: Prime Factorization of 45220

Prime factors of 45220 are 2, 5, 7, 17, 19. Prime factorization of 45220 in exponential form is:

45220 = 2² × 5¹ × 7¹ × 17¹ × 19¹

Step-3: Factors of 45200

List of positive integer factors of 45200 that divides 45200 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 113, 200, 226, 400, 452, 565, 904, 1130, 1808, 2260, 2825, 4520, 5650, 9040, 11300, 22600

Step-4: Factors of 45220

List of positive integer factors of 45220 that divides 45200 without a remainder.

1, 2, 4, 5, 7, 10, 14, 17, 19, 20, 28, 34, 35, 38, 68, 70, 76, 85, 95, 119, 133, 140, 170, 190, 238, 266, 323, 340, 380, 476, 532, 595, 646, 665, 1190, 1292, 1330, 1615, 2261, 2380, 2660, 3230, 4522, 6460, 9044, 11305, 22610

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45200 and 45220. The biggest common factor number is the GCF number.
So the greatest common factor 45200 and 45220 is 20.

Also check out the Least Common Multiple of 45200 and 45220